Grade: 6 Unit: 1 Week: 5 Content: Math Dates: 9/17-9/21/12
Theme Essential Question: How do students connect ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems?
Essential Questions:
Can students use ratio reasoning to convert from one unit of measurement to another?
Can students use ratio reasoning to convert from one unit of capacity to another?
Can students use ratio reasoning to convert from unit of weight or mass to another?
Can students transform units to solve problems?
Can students solve problems involving distance, rate, and time by applying strategies?
StandardsRatios and Proportional Relationships 6.RPUnderstand ratio concepts and use ratio reasoning to solve problems.
6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Objectives
The student will understand that measurement units employ ratio reasoning (e.g., if 3 feet is equal to yard, then 6 feet is equal to 2 yards).
The student will understand that tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations can help scaffold understanding for converting measurement units.
The student will understand that establishing connections between tools allow for extended reasoning and synthesis of the concept of ratios and rates (e.g., How do tape diagrams and double number lines show rate reasoning given the same context?).
The students will create a bingo game with measurement conversions that can be played/shared with the class. See the following websites for ideas and blank boards:
The student can convert customary units using ratio tools and methods.
The student can convert metric units by multiplying or dividing by powers of ten.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary
Unit Unit Rate Proportion Cross Products Scale Modeling Scale Drawing Rate Scale
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 6
Lessons 15-37, p.29-38
Teaching the Common Core Math Standards with Hands on Activities
http://illustrativemathematics.org/illustrations/79 The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM GP3. Unit 2, p.35-78
Glencoe
Hands on Lab 384-385
Algebra: Solving Proportions Mini Lab pg: 386
Spreadsheet Investigation pg. 390
Hands on Lab Construct Scale Drawings pg: 391
Bellringer pg. 391
Study Guide and Intervention pg. 491, 496 and 501
Calculators and Spreadsheet Masters pg 43
Key Teaching Transparencies pg 37
MathPass Tutorial CD-Rom pg 29
Real-life Career Masters pg10
Teaching Mathematics with Manipulatives pgs.91-92
Noteables Interactive Study Noteables with Foldables 10-2
Diverse Learners:
Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Math’scool: Unit C, Module 12.1,12.2, 12.3, 12.4, 12.5
Homework
See appropriate Glencoe, OnCore, JBHM, and ABC materials
Terminology for Teachers Scale-gives the ratio that compares the measurements on the drawing or model to the measurement of the real object. Scale Modeling-use to represent objects that are too large or too small to be drawn or built at actual size. Scale Drawing Rate- is a ration of two measurements having different kinds of units. Conversion factor-a rate in which the two quantities are equal but expressed in different units. Unit Rate-When a rate is simplified sp that it has a denominator of 1.
http://sciencenetlinks.com/tools/cell-size-and-scale/ This tool from Science NetLinks shares a simple interactive from the University of Utah's Genetic Science Learning Center that gives students the opportunity to see how various small things compare to one another.
Theme Essential Question: How do students connect ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems?
Essential Questions:
- Can students use ratio reasoning to convert from one unit of measurement to another?
- Can students use ratio reasoning to convert from one unit of capacity to another?
- Can students use ratio reasoning to convert from unit of weight or mass to another?
- Can students transform units to solve problems?
- Can students solve problems involving distance, rate, and time by applying strategies?
StandardsRatios and Proportional Relationships 6.RPUnderstand ratio concepts and use ratio reasoning to solve problems.- 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Objectives- The student will understand that measurement units employ ratio reasoning (e.g., if 3 feet is equal to yard, then 6 feet is equal to 2 yards).
- The student will understand that tools such as tables of equivalent ratios, tape diagrams, double number line diagrams, and equations can help scaffold understanding for converting measurement units.
- The student will understand that establishing connections between tools allow for extended reasoning and synthesis of the concept of ratios and rates (e.g., How do tape diagrams and double number lines show rate reasoning given the same context?).
Background InformationRecommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. http://www.azed.gov/standards-practices/files/2011/06/2010mathgr6.pdfOhio Dept of Education Mathematics Model Curriculum 6-28-2011Assessment
Product
- The students will create a bingo game with measurement conversions that can be played/shared with the class. See the following websites for ideas and blank boards:
http://www.educationworld.com/a_lesson/TM/WS_lp268-04.htmlhttp://www.teach-nology.com/web_tools/materials/bingo/Key Questions
- How do you convert units to length?
- How do you convert units of capacity?
- How do you convert units of weight and mass?
- How do you transform units?
Observable Student Behaviors1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unit Rate
Proportion
Cross Products
Scale Modeling
Scale Drawing
Rate
Scale
- Houghton Mifflin OnCore Mathematics Middle School Grade 6
- Lessons 15-37, p.29-38
- Teaching the Common Core Math Standards with Hands on Activities
- JBHM GP 1. Unit 1, p. 1-29
- NLVM conversion manipulative: http://nlvm.usu.edu/en/nav/frames_asid_272_g_2_t_4.html?open=instructions&from=category_g_2_t_4.html
- Highly Recommended:
http://illustrativemathematics.org/illustrations/79The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners:
Homework
- See appropriate Glencoe, OnCore, JBHM, and ABC materials
http://www.kutasoftware.com/free.htmlto print assignments on variety of topicsTerminology for Teachers
Scale-gives the ratio that compares the measurements on the drawing or model to the measurement of the real object.
Scale Modeling-use to represent objects that are too large or too small to be drawn or built at actual size.
Scale Drawing
Rate- is a ration of two measurements having different kinds of units.
Conversion factor-a rate in which the two quantities are equal but expressed in different units.
Unit Rate-When a rate is simplified sp that it has a denominator of 1.
Lesson Plan in Word Format (Click Cancel if asked to Log In)
Resources
Professional Texts
- Teaching the Common Core Math Standards with Hands on Activities
Literary TextsInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
Websites
SMART Board Lessons, Promethean Lessons
Other Activities, etc.
- Cell Size and Scale
http://sciencenetlinks.com/tools/cell-size-and-scale/This tool from Science NetLinks shares a simple interactive from the University of Utah's Genetic Science Learning Center that gives students the opportunity to see how various small things compare to one another.
- Discovering Gallon Man
http://illuminations.nctm.org/LessonDetail.aspx?ID=L513Students experiment with units of liquid measure used in the customary system of measurement. They practice making volume conversions in the customary system.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
6 Matrix
6 PAP Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-5
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6